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# proj2 - STA 4322/5328 Project 2 Spring 2010 Due Tuesday...

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STA 4322/5328 – Project 2 – Spring 2010 Due Tuesday March 2 Part 1: Acidity Levels in a Lake A biologist is interested in the acidity levels in a lake. The levels vary along a normal distribution with a mean of 6.0 and a variance of 0.16 (which she is not aware of). She is planning on sampling n=9 water specimens, and using them to estimate the mean and variance of the acidity levels for the entire lake. She proposes 2 estimators for the mean: the sample mean and the sample median. She will use the sample variance to estimate the population variance. 1. Generate 10000 random samples of n=9 from a N(6.0,0.16) distribution. 2. For each sample, obtain the sample mean, median, and variance 3. Give the mean and variance for each of the 3 estimators 4. Give histograms of each estimator 5. Give the estimated efficiency of the mean relative to the median eff(mean,median) 6. Based on the sample mean and variance, obtain 95% confidence intervals for the population mean and variance. What proportion of the intervals contain the true values?

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proj2 - STA 4322/5328 Project 2 Spring 2010 Due Tuesday...

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